PRIN.OF CORPORATE FINANCE
13th Edition
ISBN: 9781260013900
Author: BREALEY
Publisher: RENT MCG
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Chapter 26, Problem 10PS
Futures prices* In December 2017, six-month futures on the Australian S&P/ASX 200 Index traded at 5,947. Spot was 6,001. The interest rate was 1.8% a year, and the dividend yield was about 4.4% a year. Were the futures fairly priced?
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Consider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 1,950, and the June maturity contract is at F0 = 1,951.a. If the current interest rate is 2.5%, and the average dividend rate of the stocks in the index is 1.9%, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?b. Suppose now that you in fact have access to 90% of the proceeds from a short sale. What is the lower bound on the futures price that rules out arbitrage opportunities?c. By how much does the actual futures price fall below the no-arbitrage bound?d. Formulate the appropriate arbitrage strategy, and calculate the profits to that strategy.
The S&P 500 spot price is $4,570. The futures price with 6-months delivery is $4,895. The risk-less rate of return for 6-months is 3.68%.
You enter into ONE futures contract to deliver ONE index portfolio in 6-months and receive $4,895. Whatever profit you make, you transfer to today. How much $ profit will you have today?
Hint: Borrowing money today and selling risk-less bonds are equivalent actions.
Whatever $ profit you may make from the above transactions, you have to bring back to today by borrowing at the risk-less rate.
Assume no transactions costs (you can borrow and lend at the risk-less rate etc.).
Consider a six-month futures contract on the FTSE 100. Assume the stocks underlying the index provide an annual dividend yield of 6.2% and the value of the index is 6754.5.
Calculate the price of the index (to the nearest full index point) if the continuously compounded risk-free interest rate is (i) 6.9% and (ii) 5.
Chapter 26 Solutions
PRIN.OF CORPORATE FINANCE
Ch. 26 - Vocabulary check Define the following terms: a....Ch. 26 - Prob. 2PSCh. 26 - Catastrophe bonds On some catastrophe bonds,...Ch. 26 - Futures and options A gold-mining firm is...Ch. 26 - Prob. 5PSCh. 26 - Prob. 6PSCh. 26 - Futures contracts List some of the commodity...Ch. 26 - Prob. 8PSCh. 26 - Futures prices Calculate the value of a six-month...Ch. 26 - Futures prices In December 2017, six-month futures...
Ch. 26 - Prob. 11PSCh. 26 - Prob. 13PSCh. 26 - Prob. 15PSCh. 26 - Prob. 16PSCh. 26 - Prob. 17PSCh. 26 - Convenience yield In March 2018, six-month bitcoin...Ch. 26 - Prob. 19PSCh. 26 - Prob. 20PSCh. 26 - Total return swaps Is a total return swap on a...Ch. 26 - Prob. 22PSCh. 26 - Prob. 23PSCh. 26 - Hedging What is meant by delta () in the context...Ch. 26 - Hedging You own a 1 million portfolio of aerospace...Ch. 26 - Prob. 26PSCh. 26 - Prob. 27PSCh. 26 - Prob. 28PSCh. 26 - Hedging Price changes of two gold-mining stocks...Ch. 26 - Prob. 30PSCh. 26 - Prob. 31PSCh. 26 - Prob. 32PSCh. 26 - Prob. 33PSCh. 26 - You are a vice president of Rensselaer Advisers...
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- The one-year futures price on a particular stock - index portfolio is 1,124.91, the stock index currently is 1, 116, the one-year risk-free interest rate is 2.61%, and the year-end dividend that will be paid on a $1,116 investment in the index portfolio is $13.73. By how much is the contract mispriced? future price - parity pricearrow_forwardThe multiplier for a futures contract on a certain stock market index is $250. The maturity of the contract is one year, the current level of the index is 1,500, and the risk-free interest rate is 0.2% per month. The dividend yield on the index is 0.1% per month. Suppose that after one month, the stock index is at 1,533. Find the cash flow from the mark-to-market proceeds on the contract. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Cash flowarrow_forwardCurrently (on June 23) the value of August BIST 30 index futures is 1560 while the spot BIST 30 index has a value of 1512. Given that the current annual interest rate in Turkey is 20% and the annual dividend yield of the BIST 30 index is 4%; b) Is there an arbitrage gap? If so; what may be the arbitrage gain in case of an arbitrage with 50 contracts? Note: Contract Multiplier is 10arrow_forward
- The ASX200 index is currently sitting at 6458. The risk-free interest rate is 2% per annum. Exactly three months remain before the Nov-19 SPI200 futures contract expires. The SPI200 is quoted at 6410. This futures price implies that the dividend yield on the ASX200 market index is: The futures price tells us nothing about the dividend yield 2.00% 4.98% 2.48% 0.98%arrow_forwardThe Nasdaq 100 index is currently at 16.562. What is the 208 day futures price if the interest rate is 5.2% and dividend yield is 1.58%, both continuously compounded per annum?arrow_forwardSuppose the 6-month Mini S&P 500 futures price is 1,345.99, while the cash price is 1,335.81. What is the implied difference between the risk-free interest rate and the dividend yield on the S&P 500? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Implied difference %arrow_forward
- Suppose the ASX200 Index is currently at 7,406, the expected dividend yield on the index is 2 percent per year, and the risk-free rate is 0.35%. Using the current price of ASX200 futures contracts that expire in six months recommend a program trading strategy for buying or selling the futures?arrow_forwardSuppose the 6-month Mini S&P 500 futures price is 1,170.78, while the cash price is 1,158.57. What is the implied difference between the risk-free interest rate and the dividend yield on the S&P 500? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Implied difference %arrow_forward(2) The spot price of the S&P 500 index is currently at 1200 per share. The 3-month futures price is the same as the spot price. The simple interest rate is 2% for 3 months and the simple dividend yield is 1% for 3 months. (a) Calculate the arbitrage-free futures price. (b) Provide an arbitrage trading strategy.arrow_forward
- (Futures) You enter to short Japanese Yen 12,500,000 futures delivered in 6 months. The future price is F6(\/$)=116.9. If at the maturity, the spot rate is ¥93.2/$, and your position is still alive, then your profit(loss) is $_ ______. (Two decimal places.)arrow_forwardThe multiplier for a futures contract on a stock market index is $50. The maturity of the contract is 1 year, the current level of the index is 1,800, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Suppose that after 1 month, the stock index is at 1,820.a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.b. Find the holding-period return if the initial margin on the contract is $5,000arrow_forwardGiven the following quotes: FBM KLCI spot = 747 points, risk-free rate = 4.5% annualised, FBM KLCI dividend yield = 1.75% annualised. i) If the 90-day KLCI futures is quoted at 762 points, show that arbitrage is possible ii) Calculate the arbitrage profit if FBM KLCI is 10% higher by futures maturity.arrow_forward
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